Bunuel wrote:
SOLUTION
How many integers are there between, but not including, integers r and s ?
Notice that we are told that r and s are integers.
(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.
(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.
Answer: D.
Kudos points given to everyone with correct solution. Let me know if I missed someone.
I still do not understand how (1) is sufficient. My train of thought on it being insufficient is as follows with and example
s-r=10
12-2= 10 if s= 12 and r= 2 but the consecutive set could be consecutive multiples 2,4,6,8,10,12. There would only be 4 integer in between.
Do we just assume they are a consecutive set of integers?